Combinatorics

Operator (biology)

Differential algebraic equation

Mathematics

Homogeneous

Transcription factor

Partial differential equation

Gene

Distributed parameter system

Statistics

Homogeneity (statistics)

Mathematical analysis

Artificial intelligence

Repressor

Control (management)

Chemistry

Heat equation

Homogeneous differential equation

Computer science

Differential equation

Applied mathematics

Control theory (sociology)

Ordinary differential equation

Biochemistry

Hilbert space

Linear system

IEEE Transactions on Automatic Control

Based on the notion of generalized homogeneity, a new algorithm of feedback control design is developed for a plant modeled by a linear evolution equation in a Hilbert space with a possibly unbounded operator. The designed control law steers any solution of the closed-loop system to zero in a finite time. A method of homogeneous extension is presented in order to make the developed control design principles to be applicable for evolution systems with nonhomogeneous operators. The design scheme is demonstrated for the heat equation with the control input distributed on the segment [0,1].

On Homogeneous Finite-Time Control for Linear Evolution Equation in Hilbert Space